Surface force apparatus based on a spherical lens

ABSTRACT

A force detector and method for using the same includes a lens. A cantilever is disposed below the movable lens. A laser is disposed above the movable lens and is configured to emit a beam of light that reflects from a surface of the lens and the cantilever. A processor is configured to determine a force between the movable lens and the cantilever based on a change in phase in images produced by the light reflected from the spherical surface and the light reflected from the cantilever.

BACKGROUND Technical Field

The present invention relates to surface force apparatuses and, moreparticularly, to surface force apparatuses using a spherical lens andNewton's Rings to measure deflection.

Description of the Related Art

Measuring the force of attraction, or adhesion, between two surfaces isa general problem in materials science. Experimentally, measuring theinteraction between planar surfaces is challenging because the surfacesneed to be perfectly parallel. To get around this difficulty, manymeasurement techniques use curved surfaces rather than planar ones. Forexample, crossed cylinders, or a ball and a flat surface may be used tosimplify positioning. If the surfaces are smooth and if the radii ofcurvature are known, the force of interaction measured using curvedsurfaces can be related to that of two flat surfaces using, e.g., theDerjaguin Approximation.

The crossed cylinder method is used because precise alignment of thecylinder axes is not needed. The main drawback of this approach is thatspecial samples are needed. The samples must be thin (e.g., 1-2 μm) inorder to be sufficiently flexible, and they must be transparent becausethe separation between the surfaces is measured using opticaltechniques. In practice, mica is the most widely used substrate. If oneis interested in other materials, those materials must be grown ordeposited onto the mica surfaces.

Another common technique makes use of a flat surface and a sphericalsurface. The spherical surface is usually a small silica ball with aradius of only a few microns. The ball is attached to the cantilever ofan Atomic Force Microscope (AFM). The AFM is used to measure the forcebetween the ball and a macroscopic, flat surface. The main drawback ofthis approach is that it is difficult to characterize the chemical andphysical state of the ball. For example, it is difficult to determine ifthe ball is smooth or clean at such small sizes.

SUMMARY

A force detector includes a lens. A cantilever is disposed below themovable lens. A laser is disposed above the movable lens and isconfigured to emit a beam of light that reflects from a surface of thelens and the cantilever. A processor is configured to determine a forcebetween the movable lens and the cantilever based on a change in phasein images produced by the light reflected from the spherical surface andthe light reflected from the cantilever.

A method for force detection includes emitting a laser beam such thatlight reflects from a surface of a lens and a cantilever positionedbelow the lens. A force between the lens and the cantilever isdetermined with a processor based on a change in a phase in imagesproduced by the light reflected from the spherical surface and the lightreflected from the cantilever.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a diagram of a surface force measurement apparatus inaccordance with the present principles;

FIG. 2 is a diagram of a Newton's Rings interference pattern produced inaccordance with the present principles;

FIG. 3 is a diagram showing the change of ring phase in the interferencepattern corresponding with the change in distance between a lens and acantilever in accordance with the present principles;

FIG. 4 is a block/flow diagram of a surface force measurement method inaccordance with the present principles; and

FIG. 5 is a force detector control system in accordance with the presentprinciples.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the present invention employ surface force apparatusesthat include a spherical surface and a planar cantilever. According tothe present embodiments, the spherical surface is a macroscopic lens. Incontrast to the spheres used in atomic force microscopy (AFM), thespherical lens of the present embodiments is easy to characterize usingconventional microscopy and spectroscopy. A laser is directed throughthe surface of the spherical lens and reflected off the planarcantilever. The light reflected by the cantilever interferes with lightreflected from the inner surface of the lens, creating a Newton's Ringsinterference pattern that is used to determine the distance of thecantilever from the surface.

Reference in the specification to “one embodiment” or “an embodiment” ofthe present principles, as well as other variations thereof, means thata particular feature, structure, characteristic, and so forth describedin connection with the embodiment is included in at least one embodimentof the present principles. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment”, as well any other variations,appearing in various places throughout the specification are notnecessarily all referring to the same embodiment.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 1, a surface force apparatus(SFA) is shown. A spherical lens 102 is mounted to a motor 114 withnanoscale positioning capability. The motor 114 positions the lens 102relative to a planar cantilever 106, and interactions between thesurface of the lens 102 and the cantilever 106 cause a force thatresults in a deflection of the cantilever 106. This deflection ismeasured as d.

The lens 102 can be formed from any suitable transparent material havinga sufficiently small surface roughness. An exemplary surface roughnessfor the present embodiments is less than about 2 nm root-mean-squared.In one particular embodiment, a fused-silica lens may be employed. Thelens 102 may also be coated with a second material, provided that thematerial is thin and sufficiently transparent. In one exemplaryembodiment, the lens 102 may have a surface coating of indium tin oxideor hafnium oxide that is about 2 nm thick. Providing such a coating onthe surface of the lens 102 allows for measurement of forces between thesurface material and the cantilever 106.

The cantilever 106 may be formed from, for example, an oxidized siliconwafer. The thickness of the cantilever 106 should be small enough toallow for a reasonably measurable deflection. In one exemplaryembodiment, the cantilever 106 may have a thickness between about 100 μmand about 700 μm. As above, the cantilever 106 may be coated with asecond material to test the second material's interaction with the lens102. In exemplary embodiments, the cantilever 106 may be coated withsilicon oxide or hafnium oxide. The lens 102 and the cantilever 106 maybe in any suitable transparent medium including, e.g., air, water, or avacuum.

A laser 104 generates a beam of light 108 that is directed downwardthrough the lens 102. Some of the laser light 108 continues downward tothe surface of the cantilever 106 and some reflects at the surface ofthe lens 102, to produce reflected light 110 in the reverse direction.The downward laser 108 reflects off the cantilever 106 to producereflected light 112 that re-enters the lens 102. The two reflected beams110 and 112 interfere to produce Newton's Rings. The two beams areredirected using a beam splitter 118 toward a camera/processor 116,which captures an image of the interference rings and measures changesin the distance, h, between the lens 102 and the cantilever 106. Usingthis distance change and the position of the lens 102, an amount ofdeflection can be determined that corresponds to a force between thelens 102 and the cantilever 106.

In this exemplary embodiment, the spherical lens 102 may be relativelylarge (e.g., about 1-2 cm) and the cantilever 106 may be relativelythick (e.g., 100-200 μm). In one specific embodiment, a silica lens maybe used having a curvature radius of 12.9 nm. This may be compared tothe size of a sphere in AFM that may be, for example, 2.5 μm. Thecantilever 106 in this specific embodiment may be about 6 cm by about 1cm and may be formed from a relatively stiff material, such as silicon.

It should be noted that a spherical lens 102 on the centimeter scale canbe made very smooth, having an exemplary roughness of less than about 2nm. The cantilever 106, meanwhile, can be readily calibrated bymeasuring the deflection of the cantilever 106 with a known mass,determining the resonant frequency, and/or by calculation from knownelastic constants.

Referring now to FIG. 2, an example of a Newton's Rings interferencepattern 200 is shown. Newton's Rings are characterized by alternatingbright and dark rings that correspond to constructive and destructiveinterference between the reflected beams 110 and 112. The outer rings ofthe pattern are spaced more closely together than the inner rings andthere is a large spot, bright or dark, in the middle. The bright ringsof constructive interference are periodic with the ring's radiussquared, such that the rings get closer together as the radiusincreases. The ring pattern 200 can be captured using a commercialdigital camera and analyzed automatically using a computer.

Referring now to FIG. 3, the locations of maxima are shown relative tothe height h shown in FIG. 1. As the height h changes (shown here asbeing proportional to the wavelength of the beam 108), the relativephase of the interfering beams of light changes, causing the locationsof the rings' maxima to change. By measuring the position of the rings,one can determine an accurate measurement of the change in heightbetween the lens 102 and the cantilever 106. A change in height h can bedetermined by measuring a change in phase,

${{\Delta \; h} = {\frac{\Delta \; p}{2\pi}\left( \frac{\lambda}{2n_{0}} \right)}},$

where Δp is the phase change, A is the wavelength, and n₀ is the indexof refraction of the medium between the surface of the lens 102 and thecantilever 106. For example, moving from a peak to a trough in FIG. 3would represent a phase change of π that corresponds to a specificchange in height. To account for changes that cross multiple cycles, acounter may be incremented each time the phase change reaches 2π.Alternatively, the motion of a single peak may be tracked acrossmultiple cycles of phase change. This analysis of the ring pattern 200can determine the distance between the surfaces of the lens 102 and thecantilever 106 to an exemplary resolution of about 10 nm in oneembodiment.

As noted above, there are two distances at play: the distance h betweenthe lens and the surface of the cantilever, which is measured usingNewton's Rings. Another relevant distance is the distance of deflectionof the cantilever, d, which corresponds directly to the force beingexerted on the cantilever. This is determined using a known position ofthe motor 114, z, relative to some calibrated zero point z₀ where thereis no deflection, and the determined separation of the two surfaces.According to this, d=(z−z₀)+(h−h₀), where h₀ is the measured distancebetween surfaces when z is an initial value z₀. A positive value for dindicates that the cantilever 106 has deflected downward, away from thelens 102, while a negative value indicates an upward deflection, towardthe lens 102. For example, the interaction between two silicon oxidesurfaces in water is repulsive and produces a measurable downwarddeflection of the cantilever 106. On the other hand, the interactionbetween silicon dioxide and hafnium oxide in water is attractive andproduces a measurable upward deflection.

Once a value for d has been determined, this readily leads to a valuefor the force exerted on the cantilever surface 106. The force F isdetermined using a known spring constant k for the cantilever as F=kd.The force between the sphere and the plane can be used to find theinteraction energy between the two surfaces as

${W = \frac{F}{2\pi \; R}},$

where R is the radius of the spherical lens 102. This outcome is validfor any additive force and is not sensitive to the alignment between thesphere and the plane—only the force as measured by the deflectiondistance d.

Referring now to FIG. 4, a method for making a force measurement isshown. Block 402 uses motor 114 to move the lens 102 while in proximitywith the cantilever 106, keeping track of the change in motor position.Block 404 uses laser 104 to shine a beam of light through the lens 102toward the cantilever 106. Some of the light will reflect back from thespherical surface of the lens 102, while other light will reflect backfrom the cantilever 106. Block 406 captures the resulting interferencepattern and measures the distance between rings in the interferencepattern resulting from the two reflected beams using a camera 116. Block408 calculates a force between the lens and the cantilever bydetermining a distance of deflection in the cantilever 106 based on achange in the position of the lens 102 and a change in the distancebetween the lens 102 and the cantilever 106.

This technique may also be used for adhesion force measurements. Tomeasure an adhesion force, block 402 moves the lens 102 into contactwith the cantilever 106 and then begins moving back. The process of FIG.4 is then repeated, with block 402 moving farther back with eachrepetition until block 406 measures a drop-off of the force measured.This drop-off represents the cantilever 106 breaking contact with thelens 102. The last force measured before the drop-off then representsthe adhesion force between the lens 102 and the cantilever 106.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing. Computer program code for carrying out operations foraspects of the present invention may be written in any combination ofone or more programming languages, including an object orientedprogramming language such as Java, Smalltalk, C++ or the like andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The program codemay execute entirely on the user's computer, partly on the user'scomputer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer may beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection may be made to an external computer (for example, through theInternet using an Internet Service Provider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks. The computer program instructions may also beloaded onto a computer, other programmable data processing apparatus, orother devices to cause a series of operational steps to be performed onthe computer, other programmable apparatus or other devices to produce acomputer implemented process such that the instructions which execute onthe computer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblocks may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

Referring now to FIG. 5, a force detector control 500 is shown. Thecontrol 500 includes a processor 502 and a memory 504 that calculate andstore force measurements. An image acquisition module communicates withcamera 116, acquires images of the interference rings, and stores theimages in memory 504. A ring phase module 508 measures a change in phaseof the rings according to a measured distance-squared. Based on thechange in phase, a deflection module 510 determines the deflection ofthe cantilever 106 based on position change information from the motor114 and a distance between the lens 102 and the cantilever 106 using themeasured change in phase. A motor control 512 controls the motor 114 tochange the position of the lens 102.

Having described preferred embodiments of a surface force apparatusbased on a spherical lens and methods for employing the same (which areintended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope of the invention as outlined by the appended claims.Having thus described aspects of the invention, with the details andparticularity required by the patent laws, what is claimed and desiredprotected by Letters Patent is set forth in the appended claims.

What is claimed is:
 1. A force detector, comprising: a lens; acantilever disposed below the movable lens; a laser disposed above themovable lens configured to emit a beam of light that reflects from asurface of the lens and the cantilever; and a processor configured todetermine a force between the movable lens and the cantilever based on achange in phase in images produced by the light reflected from thespherical surface and the light reflected from the cantilever.
 2. Theforce detector of claim 1, wherein the lens is formed from a lens basematerial and has a coating on the surface of the lens formed from afirst material to be tested.
 3. The force detector of claim 1, whereinthe cantilever comprises a cantilever base material and has a coatingformed from a second material to be tested.
 4. The force detector ofclaim 1, further comprising a motor configured to move the lens and totrack changes in lens position.
 5. The force detector of claim 1,wherein the processor is further configured to determine a deflection ofthe cantilever based on a change in lens position and a change in adistance between the lens and the cantilever.
 6. The force detector ofclaim 5, wherein the processor is further configured to determine thechange in distance between the lens and the cantilever according to${{\Delta \; h} = {\frac{\Delta \; p}{2\pi}\left( \frac{\lambda}{2n_{0}} \right)}},$where Δh is the change in distance, Δp is the change in phase ofinterference rings in an image, λ is the wavelength of the emittedlight, and n₀ is the index of refraction of the medium between thesurface of the lens and the cantilever.
 7. The force detector of claim1, wherein the lens has a spherical surface with a radius of at least 1cm and a surface roughness of 2 nm or less and wherein the cantileverhas a thickness of at least 10 μm.
 8. The force detector of claim 1,wherein the lens is in contact with the cantilever and progressivelymoved away from the cantilever's resting position, such that a force ofadhesion causes a deflection in the cantilever and wherein the processoris further configured to repeatedly measure an adhesion force betweenthe lens and the cantilever until the cantilever breaks contact with thelens.
 9. The force detector of claim 8, wherein the processor isconfigured to determine the force of adhesion based on a last measureddeflection before the cantilever breaks contact with the lens.
 10. Amethod for force detection, comprising: emitting a laser beam such thatlight reflects from a surface of a lens and a cantilever positionedbelow the lens; determining a force between the lens and the cantileverwith a processor based on a change in a phase in images produced by thelight reflected from the spherical surface and the light reflected fromthe cantilever.
 11. The method of claim 10, wherein the lens is formedfrom a lens base material and has a coating on a lens surface formedfrom a first material to be tested.
 12. The method of claim 10, whereinthe cantilever comprises a cantilever base material and has a coatingformed from a second material to be tested.
 13. The method of claim 10,further comprising moving the lens according to a known position change.14. The method of claim 10, wherein determining the force furthercomprises determining a deflection of the cantilever based on a changein lens position and a change in a distance between the lens and thecantilever.
 15. The method of claim 14, wherein determining the forcefurther comprises determining the change in distance between the lensand the cantilever according to${{\Delta \; h} = {\frac{\Delta \; p}{2\pi}\left( \frac{\lambda}{2n_{0}} \right)}},$where Δh is the change in distance, Δp is the change in phase ofinterference rings in the captured image, λ is the wavelength of theemitted light, and n₀ is the index of refraction of the medium between asurface of the lens and the cantilever.
 16. The method of claim 10,wherein the lens has a spherical surface with a radius of at least 1 cmand a surface roughness of 2 nm or less and wherein the cantilever has athickness of at least 100 μm.
 17. The method of claim 10, furthercomprising: moving the lens into contact with the cantilever; moving thelens away from the cantilever's resting position, such that a force ofadhesion causes a deflection in the cantilever; and repeatedly measuringan adhesion force between the lens and the cantilever until thecantilever breaks contact with the lens.
 18. The method of claim 17,wherein measuring the adhesion force comprises retaining a last measuredadhesion force based on the deflection before the cantilever breakscontact with the lens.